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Determinants of BetaFormally:1. Cyclicality of Revenues

– Not the same volatility of revenues– Biotech vs. Steel

2. Operating Leverage– The mix of fixed and variable costs

3. Financial Leverage– The mix of debt and equity financing

• All three have an impact on the variability of the Net Income available to the stockholders

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1. Cyclicality of RevenuesDoes the company make• Consumer products

– βP&G = 0.52– Not very cyclical

• Office Products and Supplies – βOffice Max = 2.68– Very cyclical

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2. Degree of Operating Leverage• Mix of Fixed and Variable costs• DOL increases as fixed costs rise relative to

variable costs• DOL magnifies the effects of cyclicality on

EBIT

Formula: DOL = % D Sales

%D EBIT

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Degree of Operating LeverageThree alternatives• All Variable costs: DOL = 1.00• Half Fixed, Half Variable: DOL = 1.50• All Fixed: DOL = 2.00

  All Variable Costs Half Fixed Half Variable All Fixed CostsUnits 90 100 110 90 100 110 90 100 110Price $20 $20 $20 $20 $20 $20 $20 $20 $20 Var Costs $10 $10 $10 $5 $5 $5 $0 $0 $0 Fixed Costs $0 $0 $0 $500 $500 $500 $1,000 $1,000 $1,000

Sales $1,800 $2,000 $2,200 $1,800 $2,000 $2,200 $1,800 $2,000 $2,200 VC $900 $1,000 $1,100 $450 $500 $550 $0 $0 $0 FC $0 $0 $0 $500 $500 $500 $1,000 $1,000 $1,000 Total Costs $900 $1,000 $1,100 $950 $1,000 $1,050 $1,000 $1,000 $1,000 EBIT $900 $1,000 $1,100 $850 $1,000 $1,150 $800 $1,000 $1,200

%ΔSales -10% 10% -10% 10% -10% 10%%ΔEBIT -10% 10% -15% 15% -20% 20%DOL 1.00 1.00 1.50 1.50 2.00 2.00

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3. Financial Leverage• Mix of Debt and Equity financing• Increases as fixed interest payments rise• Financial Leverage magnifies the effects of

cyclicality on NI (and EPS)• Financial Leverage is measured by the usual

leverage measures– See Chapter 3

• Debt/Equity is the most common financial leverage measure in this context

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Financial LeverageThree alternatives• No Debt: Interest Expense = $0• Some Debt: Interest Expense = $500• High Debt: Interest Expense = $800

(These are the “All Variable Cost” example from before)

  No Debt Some Debt High DebtEBIT $900 $1,000 $1,100 $900 $1,000 $1,100 $900 $1,000 $1,100 Int Exp $0 $0 $0 $500 $500 $500 $800 $800 $800 EBT $900 $1,000 $1,100 $400 $500 $600 $100 $200 $300 Taxes (35%) $315 $350 $385 $140 $175 $210 $35 $70 $105 NI $585 $650 $715 $260 $325 $390 $65 $130 $195

%ΔEBIT -10% 10% -10% 10% -10% 10%%Δ NI -10% 10% -20% 20% -50% 50%

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More about Financial Leverage• What is the effect on the firm’s Equity Beta from

more debt?• Recall a Portfolio’s Beta is the weighted average

beta of the components • So the Company’s Total Beta is the weighted

average beta of the stocks and bonds issued to finance the company

βPortfolio = E/V βEquity + D/V βDebt

• But the Total Beta is really Asset Beta

βAssets = E/V βEquity + D/V βDebt

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Beta and Financial Leverage• We have this relationship:

βAssets = E/V βEquity + D/V βDebt

• But think about βDebt

βDebt = Cov(RDebt,RMkt)/Var(RMkt)

Covariance of debt and the market is close to zeroβDebt ≈ 0

βAssets = E/V βEquity + 0

• Since V = E + D:βAssets = E/(E + D) βEquity

βEquity = βAssets (E + D)/E

βEquity = βAssets (E/E + D/E)

βEquity = βAssets [1 + D/E]

βEquity = βAssets [1 + (1-T)D/E]

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Example: • CMG is financed only with equity (no debt)

– This referred to as an “unlevered firm”

• The beta of its stock is 1.02• What is the beta of its assets given that it has no debt?

βEquity = βAssets (1 + D/E) = βAssets (1 + 0/E) = βAssets (1)

βEquity = βAssets = 1.02

• If CMG were to issue enough debt to buy back 20% of its outstanding stock, what would happen to the beta of the remaining stock?D/E = 0.20/0.80 = 0.25βEquity = βAssets (1 + D/E) = 1.02 (1 + 0.25) = 1.275

• The market risk of the stock increases by 25%• Solely from a financing decision

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Recap: Determinants of Equity Beta1. Cyclical nature of the product2. Degree of operating Leverage

• DOL = %ΔEBIT/%ΔSales• Is this a business decision or nature of the product?

3. Financial Leverage• βEquity = βAssets (1 + D/E)

• We use βEquity to calculate RE

RE = Rf + βEquity[E(RM) – Rf]

• We Use RE to calculate WACC

WACC = WERE + WDRD(1 – TC)

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Some Beta Terminology• Corporate Finance: Equity Beta βE and Asset Beta βA

• Investments: Levered Beta βL and Unlevered Beta βU

βE = βL and βA = βU

• Corporate Finance Question:– Given the Asset Beta (βA cyclicality and DOL), what do financing

decisions do to equity risk (Equity Bata βE) and the cost of equity capital?

– βA βE

• Investments Question:– Given the Levered Beta (the CAPM beta, βL )what does the company’s

risk look like without the leverage (βU)?

– βL βU

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Calculating Unlevered Beta

Before (Corporate finance notation)• Given βA what is βE?

βE = βA [1 + (1-T)D/E]

Now (Investments notation)• Given βL what is βU?

βL = βU [1 + (1-T)D/E]

βU = βL/[1 + (1-T)D/E]

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What Happens to Equity Return?

Equity Risk:βE = βA [1 + (1 - T)D/E]βL = βU [1 + (1 - T)D/E]

Equity Return:RE = RA + (RA – RD)(1 – T)D/E

RL = RU + (RU – RD)(1 – T)D/E

(This is MMII with taxes)